IDEAS home Printed from https://ideas.repec.org/a/wly/emetrp/v89y2021i4p1753-1788.html
   My bibliography  Save this article

Sales and Markup Dispersion: Theory and Empirics

Author

Listed:
  • Monika Mrázová
  • J. Peter Neary
  • Mathieu Parenti

Abstract

We characterize the relationship between the distributions of two variables linked by a structural model. We then show that, in models of heterogeneous firms in monopolistic competition, this relationship implies a new demand function that we call “CREMR” (Constant Revenue Elasticity of Marginal Revenue). This demand function is the only one that is consistent with productivity and sales distributions having the same form (whether Pareto, lognormal, or Fréchet) in the cross section, and it is necessary and sufficient for Gibrat's Law to hold over time. Among the applications we consider, we use our methodology to characterize misallocation across firms; we derive the distribution of markups implied by any assumptions on demand and productivity; and we show empirically that CREMR‐based markup distributions provide an excellent parsimonious fit to Indian firm‐level data, which in turn allows us to calculate the proportion of firms that are of suboptimal size in the market equilibrium.

Suggested Citation

  • Monika Mrázová & J. Peter Neary & Mathieu Parenti, 2021. "Sales and Markup Dispersion: Theory and Empirics," Econometrica, Econometric Society, vol. 89(4), pages 1753-1788, July.
    • Handle: RePEc:wly:emetrp:v:89:y:2021:i:4:p:1753-1788
    DOI: 10.3982/ECTA17416
    as

    Download full text from publisher

    File URL: https://doi.org/10.3982/ECTA17416
    Download Restriction: no
    File URL: https://libkey.io/10.3982/ECTA17416?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Peter J. Klenow & Sergii Meleshchuk & Martha Denisse Pierola & Andres Rodriguez-Clare, 2018. "The Intensive Margin in Trade," IMF Working Papers 2018/259, International Monetary Fund.
    2. Pierre‐Philippe Combes & Gilles Duranton & Laurent Gobillon & Diego Puga & Sébastien Roux, 2012. "The Productivity Advantages of Large Cities: Distinguishing Agglomeration From Firm Selection," Econometrica, Econometric Society, vol. 80(6), pages 2543-2594, November.
    3. James Harrigan & Ariell Reshef, 2015. "Skill-biased heterogeneous firms, trade liberalization and the skill premium," Canadian Journal of Economics, Canadian Economics Association, vol. 48(3), pages 1024-1066, August.
    4. repec:hal:spmain:info:hdl:2441/f6h8764enu2lskk9p2m9j4i07 is not listed on IDEAS
    5. Bas, Maria & Mayer, Thierry & Thoenig, Mathias, 2017. "From micro to macro: Demand, supply, and heterogeneity in the trade elasticity," Journal of International Economics, Elsevier, vol. 108(C), pages 1-19.
    6. Jan Eeckhout, 2004. "Gibrat's Law for (All) Cities," American Economic Review, American Economic Association, vol. 94(5), pages 1429-1451, December.
    7. Feenstra, Robert C., 2018. "Restoring the product variety and pro-competitive gains from trade with heterogeneous firms and bounded productivity," Journal of International Economics, Elsevier, vol. 110(C), pages 16-27.
    8. John Sutton, 1997. "Gibrat's Legacy," Journal of Economic Literature, American Economic Association, vol. 35(1), pages 40-59, March.
    9. Monika Mrázová & J Peter Neary, 2019. "Selection Effects with Heterogeneous Firms," Journal of the European Economic Association, European Economic Association, vol. 17(4), pages 1294-1334.
    10. Swati Dhingra & John Morrow, 2012. "The Impact of Integration on Productivity and Welfare Distortions Under Monopolistic Competition," FIW Working Paper series 088, FIW.
    11. Marc J. Melitz & Giancarlo I. P. Ottaviano, 2021. "Market Size, Trade, and Productivity," World Scientific Book Chapters, in: Firms and Workers in a Globalized World Larger Markets, Tougher Competition, chapter 4, pages 87-108, World Scientific Publishing Co. Pte. Ltd..
    12. Evgeny Zhelobodko & Sergey Kokovin & Mathieu Parenti & Jacques‐François Thisse, 2012. "Monopolistic Competition: Beyond the Constant Elasticity of Substitution," Econometrica, Econometric Society, vol. 80(6), pages 2765-2784, November.
    13. Kristian Behrens & Gilles Duranton & Frédéric Robert-Nicoud, 2014. "Productive Cities: Sorting, Selection, and Agglomeration," Journal of Political Economy, University of Chicago Press, vol. 122(3), pages 507-553.
    14. Hallak, Juan Carlos & Sivadasan, Jagadeesh, 2013. "Product and process productivity: Implications for quality choice and conditional exporter premia," Journal of International Economics, Elsevier, vol. 91(1), pages 53-67.
    15. Roc Armenter & Mikl?s Koren, 2014. "A Balls-and-Bins Model of Trade," American Economic Review, American Economic Association, vol. 104(7), pages 2127-2151, July.
    16. Elhanan Helpman & Marc J. Melitz & Stephen R. Yeaple, 2004. "Export Versus FDI with Heterogeneous Firms," American Economic Review, American Economic Association, vol. 94(1), pages 300-316, March.
    17. repec:lic:licosd:30011 is not listed on IDEAS
    18. Keith Head & Thierry Mayer & Mathias Thoenig, 2014. "Welfare and Trade without Pareto," American Economic Review, American Economic Association, vol. 104(5), pages 310-316, May.
    19. Bond, Steve & Hashemi, Arshia & Kaplan, Greg & Zoch, Piotr, 2021. "Some unpleasant markup arithmetic: Production function elasticities and their estimation from production data," Journal of Monetary Economics, Elsevier, vol. 121(C), pages 1-14.
    20. Dixit, Avinash K & Stiglitz, Joseph E, 1977. "Monopolistic Competition and Optimum Product Diversity," American Economic Review, American Economic Association, vol. 67(3), pages 297-308, June.
    21. Pollak, Robert A, 1972. "Generalized Separability," Econometrica, Econometric Society, vol. 40(3), pages 431-453, May.
    22. Ina Simonovska, 2015. "Income Differences and Prices of Tradables: Insights from an Online Retailer," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(4), pages 1612-1656.
    23. Bertoletti, Paolo & Epifani, Paolo, 2014. "Monopolistic competition: CES redux?," Journal of International Economics, Elsevier, vol. 93(2), pages 227-238.
    24. Marc J. Melitz & Stephen J. Redding, 2015. "New Trade Models, New Welfare Implications," American Economic Review, American Economic Association, vol. 105(3), pages 1105-1146, March.
    25. Luís M B Cabral & José Mata, 2003. "On the Evolution of the Firm Size Distribution: Facts and Theory," American Economic Review, American Economic Association, vol. 93(4), pages 1075-1090, September.
    26. Rosa L. Matzkin, 2003. "Nonparametric Estimation of Nonadditive Random Functions," Econometrica, Econometric Society, vol. 71(5), pages 1339-1375, September.
    27. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, May.
    28. Xavier Gabaix, 2011. "The Granular Origins of Aggregate Fluctuations," Econometrica, Econometric Society, vol. 79(3), pages 733-772, May.
    29. M. C. Jones, 2015. "On Families of Distributions with Shape Parameters," International Statistical Review, International Statistical Institute, vol. 83(2), pages 175-192, August.
    30. Peter J. Klenow & Jonathan L. Willis, 2016. "Real Rigidities and Nominal Price Changes," Economica, London School of Economics and Political Science, vol. 83(331), pages 443-472, July.
    31. Thomas J. Holmes & John J. Stevens, 2014. "An Alternative Theory of the Plant Size Distribution, with Geography and Intra- and International Trade," Journal of Political Economy, University of Chicago Press, vol. 122(2), pages 369-421.
    32. Marco Bee & Stefano Schiavo, 2018. "Powerless: gains from trade when firm productivity is not Pareto distributed," Review of World Economics (Weltwirtschaftliches Archiv), Springer;Institut für Weltwirtschaft (Kiel Institute for the World Economy), vol. 154(1), pages 15-45, February.
    33. Kristian Behrens & Giordano Mion & Yasusada Murata & Jens Suedekum, 2020. "Quantifying the Gap Between Equilibrium and Optimum under Monopolistic Competition," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 135(4), pages 2299-2360.
    34. Felix Tintelnot, 2017. "Global Production with Export Platforms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 132(1), pages 157-209.
    35. Parenti, Mathieu & Ushchev, Philip & Thisse, Jacques-François, 2017. "Toward a theory of monopolistic competition," Journal of Economic Theory, Elsevier, vol. 167(C), pages 86-115.
    36. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    37. Paolo Bertoletti & Federico Etro, 2022. "Monopolistic competition, as you like it," Economic Inquiry, Western Economic Association International, vol. 60(1), pages 293-319, January.
    38. Chang-Tai Hsieh & Peter J. Klenow, 2009. "Misallocation and Manufacturing TFP in China and India," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 124(4), pages 1403-1448.
    39. Erzo G. J. Luttmer, 2011. "On the Mechanics of Firm Growth," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(3), pages 1042-1068.
    40. Robert C. Feenstra & David E. Weinstein, 2017. "Globalization, Markups, and US Welfare," Journal of Political Economy, University of Chicago Press, vol. 125(4), pages 1040-1074.
    41. Epifani, Paolo & Gancia, Gino, 2011. "Trade, markup heterogeneity and misallocations," Journal of International Economics, Elsevier, vol. 83(1), pages 1-13, January.
    42. John Haltiwanger & Robert Kulick & Chad Syverson, 2018. "Misallocation Measures: The Distortion That Ate the Residual," NBER Working Papers 24199, National Bureau of Economic Research, Inc.
    43. Kimball, Miles S, 1995. "The Quantitative Analytics of the Basic Neomonetarist Model," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 27(4), pages 1241-1277, November.
    44. repec:hal:pseose:hal-00812695 is not listed on IDEAS
    45. Costas Arkolakis & Arnaud Costinot & Andres Rodriguez-Clare, 2012. "New Trade Models, Same Old Gains?," American Economic Review, American Economic Association, vol. 102(1), pages 94-130, February.
    46. Julian di Giovanni & Andrei A. Levchenko, 2009. "International Trade and Aggregate Fluctuations in Granular Economies," Working Papers 585, Research Seminar in International Economics, University of Michigan.
    47. repec:hal:spmain:info:hdl:2441/nki2gcedn93280ns6fslbhdnm is not listed on IDEAS
    48. Chang-Tai Hsieh & Peter J. Klenow, 2007. "Relative Prices and Relative Prosperity," American Economic Review, American Economic Association, vol. 97(3), pages 562-585, June.
    49. Costas Arkolakis, 2016. "A Unified Theory of Firm Selection and Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 131(1), pages 89-155.
    50. Costas Arkolakis & Arnaud Costinot & Dave Donaldson & Andrés Rodríguez-Clare, 2019. "The Elusive Pro-Competitive Effects of Trade," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(1), pages 46-80.
    51. Ijiri, Yuji & Simon, Herbert A, 1974. "Interpretations of Departures from the Pareto Curve Firm-Size Distributions," Journal of Political Economy, University of Chicago Press, vol. 82(2), pages 315-331, Part I, M.
    52. Dasgupta, Kunal & Mondria, Jordi, 2018. "Inattentive importers," Journal of International Economics, Elsevier, vol. 112(C), pages 150-165.
    53. Swati Dhingra & John Morrow, 2019. "Monopolistic Competition and Optimum Product Diversity under Firm Heterogeneity," Journal of Political Economy, University of Chicago Press, vol. 127(1), pages 196-232.
    54. Thomas Chaney, 2008. "Distorted Gravity: The Intensive and Extensive Margins of International Trade," American Economic Review, American Economic Association, vol. 98(4), pages 1707-1721, September.
    55. Sims, Christopher A., 2003. "Implications of rational inattention," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 665-690, April.
    56. Simon Galle & Andrés Rodríguez-Clare & Moises Yi, 2023. "Slicing the Pie: Quantifying the Aggregate and Distributional Effects of Trade," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 90(1), pages 331-375.
    57. Ullah, Aman, 2002. "Uses of entropy and divergence measures for evaluating econometric approximations and inference," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 313-326, March.
    58. repec:spo:wpmain:info:hdl:2441/nki2gcedn93280ns6fslbhdnm is not listed on IDEAS
    59. Julian di Giovanni & Andrei A. Levchenko, 2012. "Country Size, International Trade, and Aggregate Fluctuations in Granular Economies," Journal of Political Economy, University of Chicago Press, vol. 120(6), pages 1083-1132.
    60. Feenstra, Robert & Kee, Hiau Looi, 2008. "Export variety and country productivity: Estimating the monopolistic competition model with endogenous productivity," Journal of International Economics, Elsevier, vol. 74(2), pages 500-518, March.
    61. Stiglitz, Joseph E, 1969. "Distribution of Income and Wealth among Individuals," Econometrica, Econometric Society, vol. 37(3), pages 382-397, July.
    62. Jonathan Eaton & Samuel Kortum, 2002. "Technology, Geography, and Trade," Econometrica, Econometric Society, vol. 70(5), pages 1741-1779, September.
    63. Nigai, Sergey, 2017. "A tale of two tails: Productivity distribution and the gains from trade," Journal of International Economics, Elsevier, vol. 104(C), pages 44-62.
    64. Paula Bustos, 2011. "Trade Liberalization, Exports, and Technology Upgrading: Evidence on the Impact of MERCOSUR on Argentinian Firms," American Economic Review, American Economic Association, vol. 101(1), pages 304-340, February.
    65. repec:spo:wpmain:info:hdl:2441/6apm7lruv088iagm4rv2c33jtg is not listed on IDEAS
    66. Christensen, Laurits R & Jorgenson, Dale W & Lau, Lawrence J, 1975. "Transcendental Logarithmic Utility Functions," American Economic Review, American Economic Association, vol. 65(3), pages 367-383, June.
    67. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    68. repec:spo:wpecon:info:hdl:2441/f6h8764enu2lskk9p2m9j4i07 is not listed on IDEAS
    69. Matsuyama, Kiminori, 2017. "Beyond CES: Three Alternative Classes of Flexible Homothetic Demand Systems," CEPR Discussion Papers 12210, C.E.P.R. Discussion Papers.
    70. A. R. Lamorgese & A. Linarello & Frederic Warzynski, 2014. "Free Trade Agreements and Firm-Product Markups in Chilean Manufacturing," Economics Working Papers 2014-16, Department of Economics and Business Economics, Aarhus University.
    71. Jovanovic, Boyan, 1982. "Selection and the Evolution of Industry," Econometrica, Econometric Society, vol. 50(3), pages 649-670, May.
    72. repec:hal:spmain:info:hdl:2441/5fjm1f1p0v93k9png4qo8ltnrf is not listed on IDEAS
    73. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(3), pages 739-767.
    74. repec:spo:wpmain:info:hdl:2441/f6h8764enu2lskk9p2m9j4i07 is not listed on IDEAS
    75. repec:hal:spmain:info:hdl:2441/2j87pv5ou185f980qgrpf9net0 is not listed on IDEAS
    76. Marc J. Melitz, 2003. "The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity," Econometrica, Econometric Society, vol. 71(6), pages 1695-1725, November.
    77. repec:hal:spmain:info:hdl:2441/6apm7lruv088iagm4rv2c33jtg is not listed on IDEAS
    78. J. A. Mirrlees, 1971. "An Exploration in the Theory of Optimum Income Taxation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(2), pages 175-208.
    79. Thibault Fally, 2018. "Integrability and Generalized Separability," NBER Working Papers 25025, National Bureau of Economic Research, Inc.
    80. repec:spo:wpmain:info:hdl:2441/5fjm1f1p0v93k9png4qo8ltnrf is not listed on IDEAS
    81. Erzo G. J. Luttmer, 2007. "Selection, Growth, and the Size Distribution of Firms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 122(3), pages 1103-1144.
    82. Per Krusell & Anthony A. Smith & Jr., 1998. "Income and Wealth Heterogeneity in the Macroeconomy," Journal of Political Economy, University of Chicago Press, vol. 106(5), pages 867-896, October.
    83. Colin Cameron, A. & Windmeijer, Frank A. G., 1997. "An R-squared measure of goodness of fit for some common nonlinear regression models," Journal of Econometrics, Elsevier, vol. 77(2), pages 329-342, April.
    84. John Haltiwanger & Ron S. Jarmin & Javier Miranda, 2013. "Who Creates Jobs? Small versus Large versus Young," The Review of Economics and Statistics, MIT Press, vol. 95(2), pages 347-361, May.
    85. Bas, Maria & Mayer, Thierry & Thoenig, Mathias, 2017. "From micro to macro: Demand, supply, and heterogeneity in the trade elasticity," Journal of International Economics, Elsevier, vol. 108(C), pages 1-19.
    86. Hopenhayn, Hugo A, 1992. "Entry, Exit, and Firm Dynamics in Long Run Equilibrium," Econometrica, Econometric Society, vol. 60(5), pages 1127-1150, September.
    87. repec:hal:wpspec:info:hdl:2441/f6h8764enu2lskk9p2m9j4i07 is not listed on IDEAS
    88. John Muellbauer, 1975. "Aggregation, Income Distribution and Consumer Demand," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 42(4), pages 525-543.
    89. Deaton, Angus S & Muellbauer, John, 1980. "An Almost Ideal Demand System," American Economic Review, American Economic Association, vol. 70(3), pages 312-326, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mrázová, Monika & Neary, J. Peter, 2020. "IO for exports(s)," International Journal of Industrial Organization, Elsevier, vol. 70(C).
    2. Peter Neary & Monika MrázováMathieu Parenti, 2015. "Technology, Demand, And The Size Distribution Of Firms," Economics Series Working Papers 774, University of Oxford, Department of Economics.
    3. Monika Mrázová & J. Peter Neary, 2017. "Not So Demanding: Demand Structure and Firm Behavior," American Economic Review, American Economic Association, vol. 107(12), pages 3835-3874, December.
    4. Ruben Dewitte & Michel Dumont & Glenn Rayp & Peter Willemé, 2022. "Unobserved heterogeneity in the productivity distribution and gains from trade," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 55(3), pages 1566-1597, August.
    5. Nigai, Sergey, 2017. "A tale of two tails: Productivity distribution and the gains from trade," Journal of International Economics, Elsevier, vol. 104(C), pages 44-62.
    6. Melitz, Marc J. & Redding, Stephen J., 2014. "Heterogeneous Firms and Trade," Handbook of International Economics, in: Gopinath, G. & Helpman, . & Rogoff, K. (ed.), Handbook of International Economics, edition 1, volume 4, chapter 0, pages 1-54, Elsevier.
    7. Ziran Ding, 2022. "Firm heterogeneity, variable markups, and multinational production: A review from trade policy perspective," Journal of Economic Surveys, Wiley Blackwell, vol. 36(5), pages 1311-1357, December.
    8. Dewitte, Ruben, 2020. "From Heavy-Tailed Micro to Macro: on the characterization of firm-level heterogeneity and its aggregation properties," MPRA Paper 103170, University Library of Munich, Germany.
    9. Paolo Bertoletti & Federico Etro, 2022. "Monopolistic competition, as you like it," Economic Inquiry, Western Economic Association International, vol. 60(1), pages 293-319, January.
    10. Gouel, Christophe & Jean, Sébastien, 2023. "Love of variety and gains from trade," European Economic Review, Elsevier, vol. 158(C).
    11. Feenstra, Robert C., 2018. "Restoring the product variety and pro-competitive gains from trade with heterogeneous firms and bounded productivity," Journal of International Economics, Elsevier, vol. 110(C), pages 16-27.
    12. Hsu, Wen-Tai & Lu, Yi & Wu, Guiying Laura, 2020. "Competition, markups, and gains from trade: A quantitative analysis of China between 1995 and 2004," Journal of International Economics, Elsevier, vol. 122(C).
    13. Etro, Federico, 2017. "Research in economics and monopolistic competition," Research in Economics, Elsevier, vol. 71(4), pages 645-649.
    14. Nocco, Antonella & Ottaviano, Gianmarco I.P. & Salto, Matteo, 2019. "Geography, competition, and optimal multilateral trade policy," Journal of International Economics, Elsevier, vol. 120(C), pages 145-161.
    15. Peter Neary & Monika Mrazova, 2013. "Not so demanding: Preference structure, firm behavior, and welfare," Economics Series Working Papers 691, University of Oxford, Department of Economics.
    16. Luca Fontanelli, 2023. "Theories of Market Selection: A Survey," GREDEG Working Papers 2023-08, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France.
    17. Macedoni, Luca & Weinberger, Ariel, 2022. "Quality heterogeneity and misallocation: The welfare benefits of raising your standards," Journal of International Economics, Elsevier, vol. 134(C).
    18. Costas Arkolakis & Arnaud Costinot & Dave Donaldson & Andrés Rodríguez-Clare, 2019. "The Elusive Pro-Competitive Effects of Trade," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(1), pages 46-80.
    19. Firooz, Hamid, 2025. "The pro-competitive consequences of trade in frictional labor markets," Journal of International Economics, Elsevier, vol. 153(C).
    20. Andrew B. Bernard & J. Bradford Jensen & Stephen J. Redding & Peter K. Schott, 2018. "Global Firms," Journal of Economic Literature, American Economic Association, vol. 56(2), pages 565-619, June.

    More about this item

    JEL classification:

    • F15 - International Economics - - Trade - - - Economic Integration
    • F23 - International Economics - - International Factor Movements and International Business - - - Multinational Firms; International Business
    • F12 - International Economics - - Trade - - - Models of Trade with Imperfect Competition and Scale Economies; Fragmentation

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:emetrp:v:89:y:2021:i:4:p:1753-1788. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/essssea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.